Study of the high pressure phase behaviour of CO2+n-alkane mixtures using the SAFT-VR approach with transferable parameters

The statistical associating fluid theory for potentials of variable range (SAFT-VR) is used to examine the phase behaviour in the CO2 + n-alkane homologous series. A unique set of transferable parameters for the unlike inter- actions are used which allow the prediction of the phase behaviour of different members of the series with little experimental data. A change in phase behaviour from type II in the van Konynenburg scheme (continuous gas–liquid critical line and liquid–liquid immiscibility at low temperatures) for CO2 + n-dodecane, to type IV (discontinuous gas–liquid critical line and liquid–liquid immiscibility) for CO2 + n-tridecane, and to type III (continuous transi- tion from gas–liquid to liquid–liquid critical behaviour) for CO2 + n-tetradecane is observed in agreement with experimental data.F.J.B. would like to thank the Oil Extraction Program of the Engineering and Physical Sciences Research Council (EPSRC) for a research fellowship (GR/N20317), and A.G. would like to thank the EPSRC for the award of an Advanced Research Fellowship. This work has also been sponsored by a research project for the VII Plan Propio de Investigación of the University of Huelva (Spain). This financial support is gratefully acknowledged

Extension of the Test-Area methodology for calculating solid-fluid interfacial tensions in cylindrical geometry

We extend the well-known Test-Area methodology of Gloor et al. [J. Chem. Phys. 123, 134703 (2005)], originally proposed to evaluate the surface tension of planar fluid-fluid interfaces along a computer simulation in the canonical ensemble, to deal with the solid-fluid interfacial tension of systems adsorbed on cylindrical pores. The common method used to evaluate the solid-fluid interfacial tension invokes the mechanical relation in terms of the tangential and normal components of the pressure tensor relative to the interface. Unfortunately, this procedure is difficult to implement in the case of cylindrical geometry, and particularly complex in case of nonspherical molecules. Following the original work of Gloor et al., we perform free-energy perturbations due to virtual changes in the solid-fluid surface. In this particular case, the radius and length of the cylindrical pore are varied to ensure constant-volume virtual changes of the solid-fluid surface area along the simulation. We apply the modified methodology for determining the interfacial tension of a system of spherical Lennard-Jones molecules adsorbed inside cylindrical pores that interact with fluid molecules through the generalized 10-4-3 Steele potential recently proposed by Siderius and Gelb [J. Chem. Phys. 135, 084703 (2011)]. We analyze the effect of pore diameter, density of adsorbed molecules, and fluid-fluid cutoff distance of the Lennard-Jones intermolecular potential on the solid-fluid interfacial tension. This extension, as the original Test-Area formulation, offers clear advantages over the classical mechanical route of computational efficiency, easy of implementation, and generality.The authors would like to acknowledge helpful discussions with A. I. Moreno-Ventas Bravo, M. M. Piñeiro, and J. M. Míguez. This work was supported by Acción Integrada España-Francia from Ministerio de Ciencia e In- novación and Picasso Project (Project Nos. FR2009-0056 and PHC PICASSO2010). Further financial support from Proyecto de Excelencia from Junta de Andalucía (Project No. P07-FQM02884), Ministerio de Ciencia e Innovación (Project No. FIS2010-14866), and Universidad de Huelva are also acknowledged

Critical behavior and partial miscibility phenomena in binary mixtures of hydrocarbons by the statistical associating fluid theory

Predictions of critical lines and partial miscibility of binary mixtures of hydrocarbons have been made by using a modified version of the statistical associating fluid theory (SAFT). The so-called soft-SAFT equation of state uses the Lennard-Jones potential for the reference fluid, instead of the hard-sphere potential of the original SAFT, accounting explicitly for the repulsive and dispersive forces in the reference term. The mixture behavior is predicted once an adequate set of molecular parameters (segment size, dispersive energy, and chain length) of the pure fluid is available. We use two sets of such parameters. The first set is obtained by fitting to the experimental saturated liquid density and by equating the chemical potential in the liquid and vapor phases for a range of temperatures and pressures. The second set is obtained from the previous one, by rescaling the segment size and dispersive energy to the experimental critical temperature and pressure. Results obtained from the theory with these parameters are compared to experimental results of hydrocarbon binary mixtures. The first set gives only qualitative agreement with experimental critical lines, although the general trend is correctly predicted. The agreement is excellent, however, when soft-SAFT is used with the rescaled molecular parameters, showing the ability of SAFT to quantitatively predict the behavior of mixtures. The equation is also able to predict transitions from complete to partial miscibility in binary mixtures containing methane.It is a pleasure to thank Dr. Allan D. Mackie, Dr. Josep Bonet-A ´ valos and Dr. Jorge Herna ´ ndez-Cobos for helpful discussions. This work was supported by DGICyT ~ PB96- 1025 ! . One of us ~ F.J.B. ! has a doctoral fellowship from Comisionat per a Universitats i Recerca from the Generalitat de Catalunya. The financial support of this fellowship is gratefully acknowledged

Surface tension of fully flexible Lennard-Jones chains: Role of long-range corrections

We have calculated the interfacial properties of fully flexible chains formed from tangentially bonded Lennard-Jones beads by direct coexistence. The full long-range tails of the potential are accounted for by means of inhomogeneous long-range corrections consisting in slice by slice summation of interactions away from the truncation sphere. We show that the corrections may be transformed into an effective long-range pair potential plus a self term, thus allowing for a fast and easy implementation of the method. After addition of the effective pair potential, the coexistence densities agree very well with results from Gibbs-ensemble simulations with usual homogeneous long-range corrections. We calculate the surface tensions without the need for explicit evaluation of the virial by using the wandering interface and test area methods. Comparison with surface tensions obtained previously for chains of truncated Lennard-Jones beads show a very large contribution of interactions beyond truncation radii as large as four bead diameters. The percentage change is about 40% for low temperatures but may increase beyond 60% for high temperatures, thus revealing the need for proper account of long-range corrections for models with untruncated interactions. The study of interfacial properties with chain length shows asymptotic increase for the surface tension and related asymptotic decrease for the interfacial width.We wish to acknowledge helpful discussions with E. de Miguel, G. Jackson, and C. Vega and P. Bryk. This work was supported by Ministerio de Educación y Ciencia through Grant Nos. FIS2007-66079-C02-01 and FIS2007-66079- C02-02. Further financial support from projects PR34/07- 15906 (Santander-UCM), CCG08-UCM/ESP-4358 (CAM– UCM), MOSSNOHO-S0505/ESP/0299 (CAM), and P07- FQM02884 (Junta de Andalucía) is also acknowledged. One of us (F.J.B.) also thanks Universidad de Huelva for additional support

Thermodynamic properties and phase equilibria of branched chain fluids using first- and second-order Wertheim’s thermodynamic perturbation theory

We present an extension of the statistical associating fluid theory (SAFT) for branched chain molecules using Wertheim’s first- and second-order thermodynamic perturbation theory with a hard-sphere reference fluid (SAFT-B). Molecules are formed by hard spherical sites which are tangentially bonded. Linear chains are described as freely jointed monomeric units, whereas branched molecules are modeled as chains with a different number of articulation points, each of them formed by three arms. In order to calculate the vapor–liquid equilibria of the system, we have considered attractive interactions between the segments forming the chain at the mean-field level of van der Waals. The Helmholtz free energy due to the formation of the chain is explicitly separated into two contributions, one accounting for the formation of the articulation tetramer, and a second one due to the formation of the chain arms. The first term is described by the second-order perturbation theory of Phan et al. [J. Chem. Phys. 99, 5326 (1993)], which has been proven to predict the thermodynamic properties of linear chain fluids in a similar manner to Wertheim’s approach. The formation of the chain arms is calculated at Wertheim’s first-order perturbation level. The theory is used to study the effect of the chain architecture on the thermodynamic properties and phase equilibria of chain molecules. The equation predicts the general trends of the compressibility factor and vapor–liquid coexistence curve of the system with the branching degree, in qualitative agreement with molecular simulation results for similar models. Finally, SAFT-B is applied to predict the critical properties of selected light alkanes in order to assess the accuracy of the theory. Experimental trends of the critical temperature of branched alkanes are qualitatively captured by this simple theory.This work was supported by the Spanish Government under Project No. PB96-1025 and VI Plan Propio de Investigación de la Universidad de Huelva. One of the authors (F.J.B.) acknowledges a doctoral fellowship from Comisionat per a Universitats i Recerca from the Generalitat de Catalunya during the course of this wor

Improved vapor–liquid equilibria predictions for Lennard-Jones chains from the statistical associating fluid dimer theory: Comparison with Monte Carlo simulations

The statistical associating fluid theory (SAFT), with monomer and dimer Lennard-Jones (LJ) reference fluids, is used to predict the phase equilibria of pure chains with different lengths. Predictions from the two versions of the theory are compared with Monte Carlo simulation results taken from the literature. We find that the additional structural information from the dimer version of the theory gives predictions in better agreement with simulation values. It is also found that the dimer version provides a much better description of the vapor pressure than the monomer one for long chains for which simulation data are available

Excess Thermodynamic Properties of Chainlike Mixtures. 1. Predictions from the Soft−SAFT Equation of State and Molecular Simulation

Monte Carlo simulation and theory are used to calculate excess thermodynamic properties of binary mixtures of Lennard-Jones chains. Chainlike molecules are formed by Lennard-Jones spherical sites that are tangentially bonded. This molecular model accounts explictly for the most important microscopic features of real chainlike molecules, such as n-alkanes: repulsive and attractive forces between chemical groups and the connectivity of segments to make up the chain. A version of the statistical associating fluid theory, the so-called Soft- SAFT equation of state, is used to check the theory’s ability to predict this kind of property. Predictions from the theory are directly compared to NPT Monte Carlo simulation results obtained in the present work. The influence of segment size, dispersive energy, and chain length on excess properties is studied using simulation and theory, and results are analyzed and discussed. The equation of state is then used to predict the general trends of some excess thermodynamic properties of real n-alkane binary mixtures, such as excess volumes and heats. In particular, the temperature and chain-length dependence of these properties is studied. The Soft-SAFT theory is found to be able to correctly describe the most important features of excess thermodynamic properties of n-alkane models

Theory of phase equilibria for model mixtures of n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock surfactants

An extension of the SAFT-VR equation of state, the so-called hetero-SAFT approach [Y. Peng, H. Zhao, and C. McCabe, Molec. Phys. 104, 571 (2006)], is used to examine the phase equilibria exhibited by a number of model binary mixtures of n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock surfactants. Despite the increasing recent interest in semifluori- nated alkanes (or perfluoroalkylalkane diblock molecules), the phase behaviour of mixtures involving these molecules with n-alkanes or perfluoroalkanes is practically unknown from the experimental point of view. In this work, we use simple molecular models for n-alkanes, perfluoroalkanes and perfluoroalkylalkane diblock molecules to predict, from a molecular perspective, the phase behaviour of selected model mixtures of perfluoroalkylalkanes with n-alkanes and perfluoroalkanes. In particular, we focus our interest on the understanding of the microscopic conditions that control the liquid–liquid separation and the stabilization of these mixtures. n-Alkanes and perfluoroalkanes are modelled as tangentially bonded monomer segments with molecular parameters taken from the literature. The perfluoroalkylalkane diblock molecules are modelled as heterosegmented diblock chains, with parameters for the alkyl and perfluoroalkyl segments developed in earlier work. This simple approach, which was proposed in previous work [P. Morgado, H. Zhao, F. J. Blas, C. McCabe, L. P. N. Rebelo, and E. J. M. Filipe, J. Phys. Chem. B, 111, 2856], is now extended to describe model n-alkane (or perfluoroalkane) þ perfluroalkylalkane binary mixtures. We have obtained the phase behaviour of different mixtures and studied the effect of the molecular weight of n-alkanes and perfluoroalkanes on the type of phase behaviour observed in these mixtures. We have also analysed the effect of the number of alkyl and perfluoroalkyl chemical groups in the surfactant molecule on the phase behaviour. In addition to the usual vapour–liquid phase separation, liquid–liquid, positive azeotropes, and Bancroft points are found for different mixtures. This rich phase behaviour is a consequence of a delicate balance between the alkyl–alkyl, perfluoroalkyl–perfluoroalkyl, and alkyl–perfluoroalkyl interactions in different molecules. We used the SAFT-VR microscopic description of chain-like systems to analyse the conditions that n-alkane (or perfluoroalkane) þ perfluoroalkyalkane mixtures should posses in order to exhibit complete liquid miscibility. Although the model proposed here is chosen to reproduce most of the quantitative features of the phase equilibria of some pure perfluoroalkylalkane diblock surfactants and their mixtures with n-alkanes, this is the first time the SAFT approach has been used to predict the phase behaviour of the mixtures considered here. The lack of experimental data for these systems does not allow us to test the accuracy of our theoretical predictions directly. However, since SAFT has proven to be an excellent approach for the prediction of the phase behaviour of complex mixtures, we expect that the theory will reproduce the most important qualitative trends exhibited by real mixtures.M.C.dR. acknowledges the programme Alßan of the European Union Programme of High Level Scholarships for Latin America (identification number E03D21773VE) for a fellowship. The authors also acknowledge financial support from project number FIS2004-06627-C02-01 of the Spanish Dirección General de Investigación. Additional support from Universidad de Huelva and Junta de Andalucía is also acknowledged. We also thank Clare McCabe and Eduardo J. M. Filipe for useful discussions

Theoretical investigation of the phase behaviour of model ternary mixtures containing n-alkanes, perfluoro-n-alkanes, and perfluoroalkylalkane diblock surfactants

We have used the hetero-SAFT-VR approach developed by McCabe and collaborators [Mol. Phys. 104, 571 (2006)] to investigate the phase equilibria of a number of binary and ternary mixtures of n-alkanes, perfluoro- n-alkanes, and perfluoroalkylalkane diblock surfactants. We focused our work on the understanding of the microscopic conditions that control the phase behaviour of these mixtures, with a particular emphasis of the effect on the liquid–liquid separation and the stabilisation of n-alkaneþperfluoro-n-alkane mixtures when a diblock surfactant is added. We used very simple molecular models for n-alkanes, and perfluoro-n-alkanes that describe the molecules as chains with tangentially bonded segments with molecular parameters taken from the literature. In the particular case of semifluorinated alkanes or SFA surfactants, we used an hetero-segmented diblock chain model where the parameters for the alkyl and perfluoroalkyl segments taken from the corresponding linear alkanes and perfluoroalkanes, as shown in our previous work [J. Phys. Chem. B 111, 2856 (2007)]. Our goal was to identify the main effects on the phase behaviour when different perfluoroalkylalkane surfactants are added to mixtures of n-alkanes and perfluoro-n-alkanes. We selected the n-hepta- neþperfluoromethane binary mixture, and studied the changes on the phase behaviour when a symmetric (same number of alkyl and perfluoroalkyl chemical groups) or an asymmetric (different number of alkyl and perfluoroalkyl chemical groups) diblock surfactants is added to the binary mixture. We have obtained the phase diagrams of a wide range of binary and ternary mixtures at different thermodynamic conditions. We have found a variety of interesting behaviours as we modify the alkyl or/and the perfluoroalkyl chain-length of the diblock surfactants: the usual changes in the vapour–liquid phase separation, changes in the type of phase diagrams (typically from type I to type V phase behaviour according to the Scott and Konynenburg classification), azeotropy, and Bancroft points. We noted that the main effect of adding a symmetric or an asymmetric surfactant to the n-heptane þ perfluoromethane mixture is to stabilise the system, i.e. to decrease the two-phase (liquid–liquid) immiscibility region of the ternary diagram as the surfactant concentration is increased. This effect becomes larger as the chain length of the surfactant is increased, which is consistent with a higher number of alkyl–alkyl and perfluoroalkyl–perfluoroalkyl favourable interactions in the mixture.M.C.dR. acknowledges the Programme Alban from European Union Programme of High Level Scholarships for Latin America (identification number E03D21773VE) for a Fellowship. Authors also acknowledge financial support from project number FIS2007-66079-C02-02 of the Spanish Dirección General de Investigación, and additional support from Universidad de Huelva and Junta de Andalucía.M.C.dR. acknowledges the Programme Al beta an from European Union Programme of High Level Scholarships for Latin America (identification number E03D21773VE) for a Fellowship. Authors also acknowledge financial support from project number FIS2007-66079-C02-02 of the Spanish Direccion General de Investigacion, and additional support from Universidad de Huelva and Junta de Andalucia